Question: What do the following two equations represent? $-3x-5y = -2$ $12x+20y = 3$
Solution: Putting the first equation in $y = mx + b$ form gives: $-3x-5y = -2$ $-5y = 3x-2$ $y = -\dfrac{3}{5}x + \dfrac{2}{5}$ Putting the second equation in $y = mx + b$ form gives: $12x+20y = 3$ $20y = -12x+3$ $y = -\dfrac{3}{5}x + \dfrac{3}{20}$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.